1.  The third equation contains a mistake. It should not contain xx. It must be x instead.

    Therefore, I re-write the system in correct form

     3x +  5y -  z + 2 = 0,
     4x -   y + 2z - 1 = 0,
    -6x - 10y + 2z = 0.

    And rewrite it one more time in the standard form:

     3x +  5y -  z = -2,    (1)
     4x -   y + 2z =  1,    (2)
    -6x - 10y + 2z =  0.    (3)


3.  Now notice that the left side of the equation (3) is exactly two times left side of the equation (1). 
    While the right side terms ARE NOT in this proportion.


    It means that the system (1),(2),(3) is INCONSISTENT, i.e. HAS NO solutions,

    Therefore, the original system, as equivalent to (1),(2),(3), HAS NO solutions as well.


Answer.  The original system is inconsistent and does not have solutions.